JEE Advanced 2017 · Paper 2, Physics question 6

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is $3 \times 10^5$ times heavier than the Earth and is at a distance $2.5 \times 10^4$ times larger than the radius of the Earth. The escape velocity from Earth’s gravitational field is $v_e = 11.2\ \mathrm{km\,s^{-1}}$. The minimum initial velocity $(v_S)$ required for the rocket to be able to leave the Sun-Earth system is closest to

(Ignore the rotation and revolution of the Earth and the presence of any other planet)